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Laguerre Derivative and Monogenic Laguerre Polynomials: An Operational Approach [PDF]

Mathematical and Computer Modelling, 2011
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I Cação
exaly   +7 more sources

Δω-Laguerre Based Appell Polynomials and Their Properties Associated With Some Special Polynomials

Applied Mathematics and Computation, 2023
In the present paper, we introduce Δω-Laguerre based Appell polynomials. The first main aim of the paper is to investigate their main properties including explicit representation, determinantal form, recurrence relation, lowering operators (LO), integro ...
Zeynep Ozat, Bayram Çeki̇M, Mehmet Ali Özarslan   +2 more
exaly   +2 more sources

Monotonicity of Zeros of Laguerre Polynomials

Journal of Computational and Applied Mathematics, 2009
Monotonicity, with respect to a parameter, of certain functions involving the zeros \(x_{nk}(\alpha)\) of the Laguerre polynomial \(L_n^{(\alpha)}(x)\) is studied. It is assumed that the zeros are arranged in decreasing order and it is proved that for any \( n \geq 2\) and \(k=1,\dots,n\), the quantities \[ \frac{x_{nk}(\alpha)-(2n+\alpha-1)}{\sqrt{2(n+
Dimitar Kolev Dimitrov, Fernando Rodrigo Rafaeli   +1 more
exaly   +4 more sources

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A Generalization of Laguerre Polynomials

SIAM Journal on Mathematical Analysis, 1993
The authors investigate orthogonal polynomials for the inner product \[ \langle p,q\rangle= \int_ 0^ \infty {x^ \alpha e^{-x}\over \Gamma(\alpha+1)} p(x)q(x) dx+Mp(0)q(0) + Np'(0) q'(0), \] thereby generalizing the Laguerre polynomials \((M=N=0)\) and Koornwinder's Laguerre-type polynomials \((N=0)\).
Koekoek, R., Meijer, H. G.
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Specializations of Generalized Laguerre Polynomials [PDF]

SIAM Journal on Mathematical Analysis, 1994
Three specializations of a set of orthogonal polynomials with ``8 different q's'' are given. The polynomials are identified as $q$-analogues of Laguerre polynomials, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
Simion, R., Stanton, D.
exaly   +4 more sources

The Addition Formula for Laguerre Polynomials

SIAM Journal on Mathematical Analysis, 1977
Bateman’s addition formula for Laguerre polynomials of order zero is generalized to the case of order $\alpha > 0$. The result is obtained as a limit case of the addition formula for disk polynomials.
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On an integral of product of laguerre polynomials

International Journal of Computer Mathematics, 1997
The evaluation of an integral of the product of Laguerre polynomials which appeared recently in this Journal by Mavromatis [36, 1990, p. 257] is shown to be a particular case of a general result of Erdelyi. An error in the special case derived earlier and other possible explicit evaluations on account of special forms of the 3 F 2(1) function are ...
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Integrals of Products of Laguerre Polynomials

SIAM Journal on Mathematical Analysis, 1975
If $L_n(x)$ is the nth Laguerre polynomial, let $A_{rst} (\alpha ) = \int _0^\infty e^{ - \alpha x} L_r (x)L_s (x)L_t (x)dx$. It has recently been shown that $A_{rst} (\alpha ) > 0$ for $\alpha \geqq 2,r,s,t = 0,1, \cdots $, while $( - 1)^{r + s + t} A_{rst} (\alpha ) \geqq 0$ for $0 0$ for $r \geqq t$. The complete conjecture has not yet been proved,
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Laguerre Polynomials

2022
Bipin Singh Koranga, Sanjay Kumar Padaliya, Vivek Kumar Nautiyal   +2 more
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Laguerre polynomials

International Journal of Mathematical Education in Science and Technology, 1979
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